1. Field of the Invention
The present invention relates to a statistical processor for performing a regression analysis with respect to sampling data.
2. Description of the Related Art
A regression analysis (least square method) for determining a function representing transition of plural data respectively having deviations is performed by calculating a regression straight line in the case of a linear function and a regression curve in the case of a function of the n-th order where n designates an integer equal to or greater than two. In the case of the regression straight line, coefficients .alpha. and .beta. are calculated by the following normal equation (1). ##EQU1##
In the case of the regression curve, especially, a regression curve of the second order, coefficients .alpha., .beta. and .gamma. are calculated by the following normal equation (2). ##EQU2##
In the equations (1) and (2), the following formulas are defined. ##EQU3##
Thus, a regression straight line function represented by Y=.alpha.+.beta.X is estimated by the calculation of the coefficients .alpha. and .beta. in the case of the linear function. A regression curve function represented by Y=.alpha.+.beta.X+.gamma.X.sup.2 is estimated by the calculation of the coefficients .alpha., .beta. and .gamma. in the case of the function of the second order.
There is a case in which supplied data are unstable and the operation of a processor is controlled to provide more stable output data in a processing for outputting data periodically processed. In such a case, there is an optimum method for controlling the operation of the processor in which the output data are fed back and transition of the output data is analyzed by the regression analysis thereof. In general, such a processing with respect to the regression analysis is performed by a microprocessor.
However, when such a processing is performed for a very short period, it is necessary to control the operation of the microprocessor using the regression analysis at a high speed. In particular, a real-time processing must be performed with respect to the regression analysis. In such a case, there are less problems when the linear function represented by a straight line are calculated since the processing is not complicated. However, when the function of the more than two order represented by a curve is calculated, it is necessary to perform many processings having more than several hundred steps so that it is impossible to perform the real-time processing by the microprocessor. For example, the respective coefficients .alpha., .beta. and .gamma. are concretely calculated by the following formulas (3) to (6). ##EQU4##